A community for students.
Here's the question you clicked on:
 0 viewing
jbritto
 3 years ago
What is the limit of (1+cosx)/sinx when x approaches 0
jbritto
 3 years ago
What is the limit of (1+cosx)/sinx when x approaches 0

This Question is Open

zugzwang
 3 years ago
Best ResponseYou've already chosen the best response.0l'Hôpital's rule, are you allowed to use that?

zugzwang
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, I panicked... no l'Hôpital's rule, I'm sorry

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2How can you use lhospital here?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow 0}\frac{1+\cos(x)}{\sin(x)}\] Recall the following: \[\lim_{x \rightarrow 0}\frac{\sin(x)}{x}=1 \text{ , } \lim_{x \rightarrow 0}\frac{\cos(x)1}{x}=0\] Let's see if we can use that here: \[\lim_{x \rightarrow 0}\frac{\cos(x)+1}{\sin(x)} \cdot \frac{\cos(x)1}{\cos(x)1}\] \[\lim_{x \rightarrow 0} \frac{\cos^2(x)1}{\sin(x)(\cos(x)1)}\] \[\lim_{x \rightarrow 0}=\frac{\sin^2(x)}{\sin(x)(\cos(x)1)}\] \[\lim_{x \rightarrow 0}\frac{\sin(x)}{\cos(x)1}\] Now try it :)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2Using L'hospital you will get something easier to look at :)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2We didn't actually need any of those things I told you to recall above :)

jbritto
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks. It still becomes 1/0 which is undefined ??

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0its not 1/0 but its 0/0 @jbritto sin0 = 0 cos0 =1

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0anyways,,there is an alternative also.. 1+ cosx = 1 + 2 cos^2 (x/2) 1 = 2cos^2 (x/2) and sinx = 2 sin(x/2) cos(x/2) so whole expression is 2 cos^2(x/2) / 2 sin(x/2) cos(x/2) = cos(x/2)/ sin(x/2) = cot (x/2) not plug in x=0

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0oh,,so you were saying it becomes 1/0 !! ohh,,am sorry.. in that case either the limit is undefined or you maybe made a typing error//

jbritto
 3 years ago
Best ResponseYou've already chosen the best response.0yes. applying LHosp rule, it will become cosx/sinx which is 1/0 undefined
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.